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Nonlinear Stochastic Evolution Equations: Analysis, Numerics and Applications

December 6th - 8th, 2018, TU Berlin

Organised by:
Etienne Emmrich
Eduard Feireisl
Raphael Kruse

Supported by Technische Universität Berlin, Einstein Center for Mathematics and German Research Foundation through DFG research unit FOR 2402.

Nonlinear evolution equations are a well-established and powerful tool to model many highly complex physical phenomena. For instance, the Navier-Stokes equations describe, besides many other applications, the turbulent flow of a liquid or gas around an obstacle. Further important examples of nonlinear evolution equations include the porous media equation in fluid mechanics, the Cahn-Hilliard equation in metallurgy, or the FitzHugh-Nagumo equation in neuroscience.

This workshop focuses on nonlinear stochastic evolution equations, which have gained a lot of attention in stochastic analysis, numerical analysis and PDE theory over the last decades. In uncertainty quantification, one introduces random coefficients or stochastic perturbations into evolution equations to model incomplete knowledge of parameter values. Often, the presence of stochastic noises lead to a low regularity of the exact solution and require new analytical and numerical methods. As one example for such a new approach we mention the rough paths theory by T. Lyons, which resulted into the development of M. Hairer's regularity structures. However, many questions, such as the regularity of solutions to nonlinear stochastic evolution equations or their numerical approximation, are often not answered yet.

Furthermore, the recent breakthrough discoveries in the field of the Euler equations and, more recently, the Navier-Stokes systems based on the application of the method of convex integration stimulate a new interest in basic questions of mathematical fluid mechanics, including a thorough revision of both modelling and suitable concepts of solutions. Here, stochastic methods could be one of possible alternative approaches to these issues.

The intension of this workshop is to bring together experts working on nonlinear stochastic evolution equations to exchange new methods and ideas on their analytical and numerical treatment and to initiate new collaborations.

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